Question

Explain in your own words the difference between a discrete random variable and continuous variable. Give a clear for example  for each that defines that distinct difference. 

What does it mean to have a success vs a failure? What the requirements for performing a binomial probability experiment? How do you find the mean and standard deviation of a binomial probability distribution? 

discussed probability, what does Do not give a formula - explain the formula itself and use an example to show this. 

Answer 1

Discrete random variables and continuous random variables have the difference between the values the random variable takes. Discrete random variable takes only the isolated values that is some particular values that have some mass we call it as probability. In other words, discrete random variable takes only countable values i.e. they may be finite or countably infinite. On the other hand, continuous random variable takes all the values in the particular interval. That is continuous random variable takes infinitely many values that are uncountable.

For example we are modelling the distribution of number of students who have failed in the previous exams. Here random variable is nimber of students who have failed. It may take values 0,1,2,3..... that is only particular values. Hence the random variable is discrete. Now suppose the distribution of the height of the students. It take all the values in the interval because the mass at any particular point or value is almost zero. Hence the random variable is continuous.

Consider any experiment having only two outcomes. That is, gender-male and female, result-pass or fail, tossing a coin-head and tail etc. In this experiment suppose we are interested in any one of the outcome then it can be treated as the success.

To use binomial distribution, the requirements are, we have the experiment which have only two outcomes and we have repeated this experiment some number of times say n with same probability of success for each trial.

Mean for the binomial distribution is n*p that is the number of times the success occurs in n trials. And standard deviation is n*p*(1-p).